THEORY OF THE MAGNETIC FORM FACTOR IN REDUCED-MOMENT KONDO SYSTEMS

Abstract

The magnetic form factor in Kondo systems, as measured by polarized neutron elastic scattering, is uniformly reduced (with respect to the atomic form factor in the crystal field) due to the Kondo effect, and moreover it shows deviations at small scattering vector due to a spin polarization of conduction electrons: the sign of the deviations in Ce compounds is positive, which is opposite to what is observed in normal rare earths of the first half of the series, and expected from the s-f exchange Hamiltonian. In the present work the above two anomalies are interpreted within a theory for the magnetic form factor in Kondo systems. The uniform reduction of the form factor follows from a variational calculation for the one-impurity Anderson model in an effective magnetic field: Kondo reduction of the localized moment is distinguished here from the presence of a screening cloud, which cannot be observed by neutron scattering. The conduction electron polarization is first studied for the Coqblin-Schrieffer Hamiltonian, which we find to lead again to negative deviations of the form factor. Within the Anderson impurity model, the conduction electron contribution to the form factor is found to be the sum of two terms: a negative RKKY-like polarization, and a positive superexchange term, which is nonzero even for a filled (or empty) band. Dominance of the superexchange polarization could explain the observed sign of the deviations in Ce compounds. A variational basis which describes both Kondo reduction and conduction electron polarization effects is studied: the two effects are clearly separated, since they appear in different orders of the calculations. The conduction electron polarization is shown to be reduced due to the Kondo effect by the same spin-fluctuation factor which reduces the localized moment.